If I had to prep in a PURELY SURVIVAL MODE in the short term and ONLY HAD $100 to budget...i.e, a situation where I had to see how well prepped I could be w/ $100...
Even if I was staying in a house or apt, I'd try to obtain the necessary 'tools' to make it OK outdoors, like a homeless person.
*Making, collecting, storing, filtering, potable water would be a top priority.
I'd get a ceramic water filter, the one for about $25 that's posted on here recently. Off ebay. And some cheap tubing to make up a gravity water supply.
If it didn't have time to wait for shipping I'd head to a store where the expensive hiking filters are sold and see if there wasn't a replacement cartridge I could rig up as a gravity filter. Maybe on closeout or just not very expensive. [Interesting, I think I'll research this a bit more] I wouldn't blow my budget on an out of the box filter, nosiree...
Next I'd make sure I had clothes to survive outside and some covering. I'd try to scrounge that w/out any $$ spent. Or Thrift store/Goodwill.
Also a full sized sheet and pillow case and some sort of backpack or something that could be used for one and something I could rip up for webbing. Some material for rags for washing and wiping, blowing my nose, etc.
Footgear, same places. Plastic sheeting, plastic garbage bags. I'd ask in a store to see if someone would give me something that was being thrown away so I can stretch my budget.
Then I'd head back to the Goodwill or thrift store and get a couple pots and utensils, and containers for water, selected based on the senario I thought likely. I'd look for a knife for food prep and and another for heavier work. I'd want a hatchet.
Also a small saw of some sort, a cheap sawzall blade and some tape would do to start. While at the hardware store I'd get some 1/8 nylon rope and some picture wire for snares. Cheapest stuff I could see.
At the same time, I'd be on the lookout to buy the best AA or 2 xAA LED flashlight I saw, probably abt $5. And find some cheap AA batteries.
I'd be worrying about stockpiling some calories. Best place might be the dollar store and I'd get a couple cans of meat, veggies and oatmeal. I'd budget $35 for that. I wouldn't eat it unless I wasn't able to scrounge food during the day.
Also, personal higyne [sp] is high on the list. I'd get some soap from a public restroom to put into a bottle from the garbage, and some paper items. A toothbrush when I stumbled over one. I'd brush with soap if I had to.
I'd constantly be on the llokout for med supplies and in the event I got sick from something that antibiotics would fix and didn't have access to med care, I'm use the antibiotics from a pet store, farm store or Walmart.
An important need would be a safe place to store my preps when I was out looking for more. I'd network with folks to find one.
Every dumpster, trash heap, would be considered like a Christmas present, an opportunity to be opened.
Another important item I' d want to find would be a bicycle. Very important and I think I have the ability to meet folks and get one for little $$$ or even have an old one given to me.
Now TOOLS. Initially, I try to get a $2 pair of imported vicegrips with wire cutters, screwdrivers, large and small, phillips and slotted.
During this time I'd be trying to develop relationships w/ most folks I came in contact with to trade my labor/skills for any kind of handout/resource and also develop long term relationships with them and help them any way I could.
Eventually, I'd probably get lucky and hook up with a nice store cash register or stock clerk girl and she'd take me home and fix me a sammich, give me a needed bath, and tuck me into her nice warm bed.
[Well, hey, I've done it before...]
Seriously, I think I could be dropped into any city in a stable time and be on my feet in days.
In a year, barring ill health and economic collapse, I would be prosperous.
If there were economic collapse, I would try to look for opportunities to outperform my peers.
This may be somewhat diverging from "what preps would you buy if you had $100" but I sorta got on a roll. But this is close to what I would actually do to survive.
To the OP, to prepare to survive, take the concepts I've written about and scale them/adjust them to your own life situation. This isn't about what and how much you can stockpile, this about a much broader field. Acquiring knowledge and good people skills will be as important if not moreso than how many sacks of rice are in your basement.
The principles are always the same, throughout history.